In order to obtain the transport efficiency, we start to calculate
the steady state dissipation rate \(\dot{W}\) . Based on the framework
of stochastic thermodynamics [1]}, [2]}, [3]}, [4]}, [5]},
the entropy balance equation reads as \(\dot{s}_{tot}(\tau )=\dot{s}_{m}(\tau )+\dot{s}(\tau )\) ,
where \(s_{tot}(\tau )\)  \(s(\tau )\)  is the Shannon entropy and \(s_{m}(\tau )\) 
is the entropy flux. As \(s(\tau )=-\ln p\left(\mathbf {x},\tau \right)\) ,
the change rate of the Shannon entropy is
\(\dot{s}(\tau )=\left[-\partial _{\tau }p(\mathbf {x},\tau )+\frac{2V}{p(\mathbf {x},\tau )}\sum _{i,j}\Gamma _{ij}J_{j}|_{\mathbf {x}(\tau )}\dot{x}_{i}\right]-V\sum _{i}H_{i}\dot{x}_{i},\) 
